[[Natural transformation]]
# Identity as a natural transformation

A rather trivial but nice result:
If $\cat C$ is a category, $1_{\cat C} : \cat C \to \cat C$ is the [[identity functor]] and $\id \in \cat C^{\cat C}(1_{\cat C}, 1_{\cat C})$ is taken to donate the corresponding [[Identity natural transformation]], 
then the notation $\id_{X}$ for the identity morphism of an object $X \in \cat C$ agrees with the component of $\id$ in $X$. #m/thm/cat 


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